easy, if your ok with browsers games check out urbandead, it's a sick game set in the city of malten I've played it for 2 years and am quite pround of my statis as a senor player.  Basicly it's a mmorpg with humans and zombies if you die as a human you rise as the zombie and can in turn be revived by a NecroTech Scientist.  Plenty of Skills to learn and updated very reguarly, it's a well done site.  And nothing compares to the bliss of eating a newplayer knowing you just ruined there day though this has been lessened with the new revive zone in graveyards.  pitty but hey make it easier for you in the begining I'm deadhead108. check it out.

One more thing, check out DeadFrontier it's a real time action MMORPG that's new.  seems real buggy but is free and has potential to be the greatest contribution to zombie games.  but no you cannot be a zombie, but you can be a Lawyer  or my personal favorite Policeman.  and just one more game that comes to mind Resident Evil oh $#^% I can't remeber the name.  But on it you can become a zombie when killed and eat your friend if your online.  Its for PS2 and my friend say's that the online is brutal your allies leaving you to die very often a real fend for yourself kind of game.